Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

mahela007

  • 3 years ago

Do the lectures specify at any point the definition of a 'Differentiable function'? The concept was used in a example and a recitation session..

  • This Question is Closed
  1. ac7qz
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    A "differentiable function" is one which is continuous over all the values of x you're interested in, and its derivative is also continuous. This means there are no sharp corners in the original function, only smooth transitions.

  2. Tebello
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Differentiation is defined by a limit, and limits need not always exist. If the limit \[\lim_{h \rightarrow 0} \frac{f(x+h) - f(x)}{h}\] exists at a particular x value then we say the function is differentiable at that point. It it exists for all x in an interval then it is differentiable on that interval. Note that the limit is double sided, so implicit in this definition is the fact that no function defined on a closed interval can be differentiable on that closed interval, thus why the wording of many of the basic theorems insist on certain intervals being open...

  3. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.